Alaska flagAlaska: Expressing Geometric Properties with Equations Math Standards

0 standards · 7 domains

DETERMINE OR DERIVE THE EQUATION OF A CIRCLE OF GIVEN CENTER AND RADIUS USING THE PYTHAGOREAN THEOREM; COMPLETE THE SQUARE TO FIND THE CENTER AND RADIUS OF A CIRCLE GIVEN BY AN EQUATION.

    DETERMINE OR DERIVE THE EQUATION OF A PARABOLA GIVEN A FOCUS AND DIRECTRIX.

      (+) DERIVE THE EQUATIONS OF ELLIPSES AND HYPERBOLAS GIVEN FOCI AND DIRECTRICES.

        PERFORM SIMPLE COORDINATE PROOFS. FOR EXAMPLE, PROVE OR DISPROVE THAT A FIGURE DEFINED BY FOUR GIVEN POINTS IN THE COORDINATE PLANE IS A RECTANGLE; PROVE OR DISPROVE THAT THE POINT (1, ROOT 3) LIES ON THE CIRCLE CENTERED AT THE ORIGIN AND CONTAINING THE POINT (0, 2).

          PROVE THE SLOPE CRITERIA FOR PARALLEL AND PERPENDICULAR LINES AND USE THEM TO SOLVE GEOMETRIC PROBLEMS (E.G., FIND THE EQUATION OF A LINE PARALLEL OR PERPENDICULAR TO A GIVEN LINE THAT PASSES THROUGH A GIVEN POINT).

            FIND THE POINT ON A DIRECTED LINE SEGMENT BETWEEN TWO GIVEN POINTS THAT PARTITIONS THE SEGMENT IN A GIVEN RATIO.

              USE COORDINATES TO COMPUTE PERIMETERS OF POLYGONS AND AREAS OF TRIANGLES AND RECTANGLES, E.G., USING THE DISTANCE FORMULA.

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